Based on Talbot effect of optical microgratings, we report an ultra-compact sensor for displacement and vibration measurement with resolution down to sub-nanometer level. With no need of optical components such as reflectors, splitters, polarizers, and wave plates, the proposed sensor based on a common-path structure shows a high compactness. Using gratings with period of 3 µm, displacement measurement within a range of 1 mm is demonstrated experimentally. Associated with an interpolation circuit with subdividing factor of 4096, a resolution of 0.73 nm is obtained. The experimental results also show the ability for the sensor to detect in-plane vibration with frequency below 900 Hz. With a sub-nanometer resolution and an ultra-compact structure, the miniature sensor shows potential in applications such as high-precision machinery manufacturing and semiconductor processing.

Here, we report an ultracompact angular displacement sensor based on the Talbot effect of optical microgratings. Periodic Talbot interference patterns were obtained behind an upper optical grating. By putting another grating within the Talbot region, the total transmission of the two-grating structure was found to be approximatively in a linear relationship with the relative pitch angle between the two gratings, which was explained by a transversal shift of the Talbot interference patterns. The influence of the grating parameters (e.g., the grating period, the number of grating lines and the gap between the two gratings) was also studied in both a simulation and an experiment, showing a tunable sensitivity and range by simply changing the grating parameters. A sensitivity of 0.19 mV/arcsec was experimentally obtained, leading to a relative sensitivity of 0.27%/arcsec within a linear range of ± 396 arcsec with the 2 μm-period optical gratings. Benefitting from tunable properties and an ultracompact structure, we believe that the proposed sensor shows great potential in applications such as aviation, navigation, robotics and manufacturing engineering.

Based on the Talbot effect of optical gratings, we propose a novel out-of-plane optical displacement sensor with an ultracompact structure, to the best of our knowledge. Using two optical gratings with a slight angle between them, two angular-modulated signals with a phase difference of 90° are obtained associated with a two-quadrant photodetector, which are in sinusoidal relationship with the displacement in the direction perpendicular to the grating plane. Using an interpolation subdivision circuit with a subdivision factor of 1000, out-of-plane displacement measurement with a resolution of 11.23 nm within a range of 1 mm is obtained.